
134Identity in Physics: A Historical, Philosophical, and Formal AnalysisOxford University Press. 2006.Steven French and Decio Krause examine the metaphysical foundations of quantum physics. They draw together historical, logical, and philosophical perspectives on the fundamental nature of quantum particles and offer new insights on a range of important issues. Focusing on the concepts of identity and individuality, the authors explore two alternative metaphysical views; according to one, quantum particles are no different from books, tables, and people in this respect; according to the other, th…Read more

2Quantum Nonindividuality: Background Concepts and PossibilitiesIn Wuppuluri Shyam & Francisco Antonio Dorio (eds.), The Map and the Territory: Exploring the Foundations of Science, Thought and Reality, Springer. pp. 281305. 2018.It is not an exaggeration to say that quantum mechanics is at odds with most of our received metaphysical notions. In particular, an alleged revision is brought about by the theory on the metaphysical notion of ‘individuality’. Certainly, this should figure as being of great interest for metaphysicians and philosophers of science alike. What makes issues even more interesting is that some of the founding fathers of the theory, with their typical philosophical inclinations, suggested that the ent…Read more

235The physics and metaphysics of identity and individuality Content Type Journal Article DOI 10.1007/s1101601094637 Authors Don Howard, Department of Philosophy and Graduate Program in History and Philosophy of Science, University of Notre Dame, Notre Dame, IN 46556, USA Bas C. van Fraassen, Philosophy Department, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA Otávio Bueno, Department of Philosophy, University of Miami, Coral Gables, FL 33124, USA Elena Caste…Read more

22Quasitruth is typically advanced as a framework accounting for incompleteness and uncertainty in the actual practices of science. Also, it is said to be useful for accommodating cases of inconsistency in science without leading to triviality. In this paper, we argue that the given developments do not deliver all that is promised. We examine the most prominent account of quasitruth available in the literature, advanced by da Costa and collaborators in many places, and argue that it cannot legit…Read more

44Following J.Y.Béziau in his pioneer work on nonstandard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in [1]. Our conclusion was that such states are contraries, contradicting previous analyzes that have led to different results, such as those claiming that those states represent contradictory properties. In this chapter we bring the …Read more

38Does Newtonian Space Provide Identity to Quantum Systems?Foundations of Science 24 (2): 197215. 2019.Physics is not just mathematics. This seems trivial, but poses difficult and interesting questions. In this paper we analyse a particular discrepancy between nonrelativistic quantum mechanics and ‘classical’ space and time. We also suggest, but not discuss, the case of the relativistic QM. In this work, we are more concerned with the notion of space and its mathematical representation. The mathematics entails that any two spatially separated objects are necessarily different, which implies that…Read more

11It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default, sheaf theory, topos theory, and nonstandard or signed probabilities. In this paper we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we…Read more

15Nonrelativistic quantum mechanics is grounded on ‘classical’ space and time. The mathematical description of these con cepts entails that any two spatially separated objects are necessarily dif ferent, which implies that they are discernible — we say that the space is T2, or "Hausdorff". But quantum systems, in the most interesting cases, some times need to be taken as indiscernible, so that there is no way to tell which system is which, and this holds even in the case of fermions. But in th…Read more

10This is a general philosophical paper where I overview some of my ideas concerning the nonreflexive foundations of quantum mechanics. By NRFQM I mean an interpretation of QM that considers an involved on tology of nonindividuals as explained in the text. Thus, I do not endorse a purely instrumentalist view of QM, but believe that it speaks of something, and then I try to show that one of the plausible views of this ‘something’ is as entities devoided of identity conditions.

23In this work we discuss logical structures related to indistinguishable particles. Most of the framework used to develop these structures was presented in [17, 28] and in [20, 14, 15, 16]. We use these structures and constructions to discuss possible ontologies for identical particles. In other words, we use these structures in order to characterize the logical structure of quantum systems for the case of indistinguishable particles, and draw possible philosophical implications. We also review s…Read more

103In this paper, we examine the concept of particle as it appears in quantum ﬁeld theories, focusing on a puzzling situation regarding this concept. Although quantum ‘particles’ arise from ﬁelds, which form the basic ontology of QFT, and thus a certain concept of ‘particle’ is al ways available, the properties ascribed to such ‘particles’ are not completely in agreement with the mathematical and logical description of such ﬁelds, which should be taken as individuals.

1401Scientific Theories, Models and the Semantic ApproachPrincipia: An International Journal of Epistemology 11 (2): 187201. 2007.According to the semantic view, a theory is characterized by a class of models. In this paper, we examine critically some of the assumptions that underlie this approach. First, we recall that models are models of something. Thus we cannot leave completely aside the axiomatization of the theories under consideration, nor can we ignore the metamathematics used to elaborate these models, for changes in the metamathematics often impose restrictions on the resulting models. Second, based on a paralle…Read more

69In this first paper of a series of works on the foundations of science, we examine the significance of logical and mathematical frameworks used in foundational studies. In particular, we emphasize the distinction between the order of a language and the order of a structure to prevent confusing models of scientific theories with firstorder structures, and which are studied in standard model theory. All of us are, of course, bound to make abuses of language even in putatively precise contexts. Th…Read more

Quasiset theories for microobjects: A comparisonIn Elena Castellani (ed.), Interpreting Bodies, Princeton University Press. pp. 14252. 1998.

82Quantum Sortal PredicatesSynthese 154 (3). 2007.Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of 'sortal' as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates 'quantumsortal predicates' and, instead of a process of counting, to them is a…Read more

77Scientific Theories, Models and the Semantic ApproachPrincipia: An International Journal of Epistemology 11 (2): 187201. 2007.According to the semantic view, a theory is characterized by a class of models. In this paper, we examine critically some of the assumptions that underlie this approach. First, we recall that models are models of something. Thus we cannot leave completely aside the axiomatization of the theories under consideration, nor can we ignore the metamathematics used to elaborate these models, for changes in the metamathematics often impose restrictions on the resulting models. Second, based on a paralle…Read more

30The Quasilattice of Indiscernible ElementsStudia Logica 97 (1): 101126. 2011.The literature on quantum logic emphasizes that the algebraic structures involved with orthodox quantum mechanics are non distributive. In this paper we develop a particular algebraic structure, the quasilattice (Jlattice), which can be modeled by an algebraic structure built in quasiset theory Q. This structure is non distributive and involve indiscernible elements. Thus we show that in taking into account indiscernibility as a primitive concept, the quasilattice that 'naturally' arises is …Read more

64A obra de Newton C.A. Da Costa em LogicaTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 7 (13): 347386. 1992.In this paper we present an overview of Professor Newton C. A. da Costa’s work in logic, emphasizing the main results obtained by him in the several areas of his research activity. The text furnish a detailed bibliographic reference of his works, which are listed in the last section

Classical Logic or NonReflexive Logic?: A Case of Semantic UnderdeterminationRevista Portuguesa de Filosofia 68 (12): 7386. 2012.

59From primitive identity to the nonindividuality of quantum objectsStudies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 46 (2): 273282. 2014.We consider the claim by Dorato and Morganti 591–610) that primitive individuality should be attributed to the entities dealt with by nonrelativistic quantum mechanics. There are two central ingredients in the proposal: in the case of nonrelativistic quantum mechanics, individuality should be taken as a primitive notion and primitive individuality is naturalistically acceptable. We argue that, strictly understood, naturalism faces difficulties in helping to provide a theory with a unique princ…Read more

21Física e OntologiaDiscusiones Filosóficas 9 (12). 2008.objeto físicolas teorías físicas. En la medida en quela física se ocupa de los constitutivosesencial. A pesar de que la física actual node explicar por qué el mundo es comolas físicas

27A discussion on quantum nonindividualityJournal of Applied NonClassical Logics 22 (12): 105124. 2012.In this paper we consider the notions of structure and models within the semantic approach to theories. To highlight the role of the mathematics used to build the structures which will be taken as the models of theories, we review the notion of mathematical structure and of the models of scientific theories. Then, we analyse a casestudy and argue that if a certain metaphysical view of quantum objects is adopted, one seeing them as nonindividuals, then there would be strong reasons to ask for a…Read more

92Some of the forerunners of quantum theory regarded the basic entities of such theories as 'nonindividuals'. One of the problems is to treat collections of such 'things', for they do not obey the axioms of standard set theories like Zermelo Fraenkel. In this paper, collections of objects to which the standard concept of identity does not apply are termed 'quasisets'. The motivation for such a theory, linked to what we call 'the Manin problem', is presented, so as its specific axioms. At the en…Read more

Quantum objects are vague objectsSorites 6 (1): 2133. 1996.Is there vagueness in the world? This is the central question that we are concerned with. Focusing on identity statements around which much of the recent debate has centred, we argue that `vague identity' arises in quantum mechanics in one of two ways. First, quantum particles may be described as individuals, with `entangled' states understood in terms of nonsupervenient relations. In this case, the vagueness is ontic but exists at the level of these relations which act as a kind of `veil'. Sec…Read more

17Sobre uma fundamentação não reflexiva da mecânica quânticaScientiae Studia 10 (1): 71104. 2012.

16Paraconsistent logics are logics that can be used to base inconsistent but nontrivial systems. In paraconsistent set theories, we can quan tify over sets that in standard set theories, if consistent, would lead to contradictions, such as the Russell set, R = fx : x =2 xg. Quasiset theories are mathematical systems built for dealing with collections of indiscernible elements. The basic motivation for the development of quasiset theories came from quantum physics, where indiscernible entities …Read more

Federal University of Santa CatarinaProfessor
University of São Paulo
Department of Philosophy, Languages and Literature, and Human Sciences
PhD, 1990
Florianópolis, Santa Catarina, Brazil
Areas of Specialization
Logic and Philosophy of Logic 
Philosophy of Physical Science 